1. Field of the Invention
The present invention relates to waveguides composed of three-dimensional photonic crystals having a three-dimensional refractive index periodic structure and also to devices including the waveguides.
2. Description of the Related Art
Yablonovitch has proposed the idea of controlling transmission/reflection characteristics for electromagnetic waves using subwavelength structures (see Physical Review Letters, Vol. 58, p. 2059, 1987). According to the document, transmission/reflection characteristics for electromagnetic waves can be controlled using periodic subwavelength structures. This control is also possible for light, that is, electromagnetic waves having wavelengths on the order of those of light. This document suggests that such structures, known as photonic crystals, facilitate the realization of a reflective mirror with a reflectance of 100%, which means no optical loss, in a certain wavelength range. The concept of providing a reflectance of 100% in a certain wavelength range is known as a photonic bandgap from an analogy to an energy gap of a semiconductor.
A three-dimensional subwavelength periodic structure can provide a photonic bandgap for light incident in any direction. Such a photonic bandgap is hereinafter referred to as a complete photonic bandgap. A complete photonic bandgap can be used to realize optical elements having new functions. For example, a photonic crystal having a point or linear defect in its periodic structure can operate as a resonator or a waveguide. In particular, it has been known that a sharply curved waveguide or an add-drop waveguide can be provided by forming a linear defect so that it can reliably trap light (see Japanese Patent Laid-Open No. 2001-74955 and Extended Abstracts of the 65th Autumn Meeting of the Japan Society of Applied Physics, No. 3, p. 936).
FIGS. 21A to 21F show three-dimensional photonic crystal structures capable of providing a complete photonic bandgap. FIG. 21A shows a diamond opal structure. FIG. 21B shows a woodpile structure. FIG. 21C shows a spiral structure. FIG. 21D shows a special three-dimensional structure. FIG. 21E shows an inverse three-dimensional periodic structure. FIG. 21F shows a diamond woodpile structure.
For a waveguide composed of a three-dimensional photonic crystal having a complete photonic bandgap, its photonic bandgap generally includes a frequency range where light propagates in a single mode and a frequency range where light propagates in multiple modes. A single mode herein refers to a mode where light of certain wavelength propagates through the waveguide with a single wave vector. Each propagation mode has its own periodic electromagnetic field intensity distribution in the waveguide.
A waveguide used for optical circuits and light-emitting devices, for example, requires a light-trapping effect and the ability to facilitate the propagation of light of a desired wavelength in a single mode. In addition, a single-peaked electromagnetic field intensity distribution symmetrical in a plane perpendicular to a propagation direction is desired for light emitted from an end of the waveguide. The electromagnetic field intensity distribution of the light emitted from the end of the waveguide depends on the electromagnetic field intensity distribution of each propagation mode in the plane perpendicular to the propagation direction at the end of the waveguide. Accordingly, a propagation mode is desired which has a single-peaked electromagnetic field intensity distribution highly concentrated in a certain area in the plane perpendicular to the propagation direction.
Japanese Patent Laid-Open No. 2001-74955 discusses a waveguide having a linear defect in its woodpile structure, as shown in FIG. 21B. The linear defect is formed by removing part of a columnar structure included in the woodpile structure. According to this publication, the waveguide structure facilitates single-mode propagation with a nearly single-peaked electromagnetic field intensity distribution in a particular frequency range. This waveguide, however, can have a limited frequency range available because light propagates in multiple modes in part of the frequency range of the photonic bandgap thereof. In addition, the photonic bandgap and the frequency range that facilitates single-mode propagation are significantly narrowed if the three-dimensional photonic crystal is composed of a medium with a low refractive index.
Extended Abstracts of the 65th Autumn Meeting of the Japan Society of Applied Physics, No. 3, p. 936 discuss a waveguide structure that facilitates the propagation of light in a single mode in a relatively wide frequency range. FIG. 22A shows the electromagnetic field intensity distribution of the light in a plane perpendicular to a propagation direction. FIG. 22B shows the electromagnetic field intensity distribution of the light in a plane parallel to the propagation direction and a stacking direction. In FIGS. 22A and 22B, central white areas represent higher electromagnetic field intensity. FIG. 22A shows a double-peaked electromagnetic field intensity distribution that is highly concentrated on additional columnar structures. The double-peaked distribution is undesirable in terms of application. FIG. 22B shows that the electromagnetic field intensity distribution varies largely along the waveguide structure. If the waveguide structure is disposed in the three-dimensional photonic crystal in combination with another resonator or waveguide structure, even slight variations in the positions of the structures due to manufacturing errors, for example, largely vary the electromagnetic field intensity distributions thereof. The properties of propagation of electromagnetic fields between the structures depend on the positional relationship between the electromagnetic field intensity distributions thereof. Even slight variations in the positions of the structures largely vary the properties of propagation of electromagnetic fields between the structures, thus significantly varying device performance. Accordingly, manufacture of devices having the waveguide structure with desired performance requires a sophisticated manufacturing technology because individual structures must be positioned with high accuracy.
Furthermore, the two waveguide structures described above cannot provide single-mode propagation in a desired frequency range because no technique is available to change the frequency of propagation mode.